Answer :
Sure! Let's go through the solution step-by-step.
We have the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Distribute and simplify both sides.
On the left side:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - 7
\][/tex]
So, the left side becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
On the right side:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify to:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: The equation now is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract 4 from both sides to isolate the terms involving [tex]\( x \)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\( x \)[/tex] that satisfies the equation is [tex]\( 0 \)[/tex].
We have the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Distribute and simplify both sides.
On the left side:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - 7
\][/tex]
So, the left side becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
On the right side:
[tex]\[
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify to:
[tex]\[
\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: The equation now is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract 4 from both sides to isolate the terms involving [tex]\( x \)[/tex]:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\( x \)[/tex] that satisfies the equation is [tex]\( 0 \)[/tex].
